
where we linearized \(f_t(x)\) . Function \(r_t\!:\!\mathcal {X}\!\mapsto \! \mathbb {R}\)  is a proximalRegularizer \(r_t(x)\)  is called proximal with reference to an algorithm that yields \(\lbrace x_t\rbrace \)  if \(x_t\!\in \!\arg \min _{x\in \mathcal {X}} r_{t}(x)\) ; and non-proximal otherwise [1]}. primal regularizer and \(q_t:\!\mathbb {R}_+^d\!\mapsto \! \mathbb {R}\)  a non-proximal dual regularizer. We also set \(\mathcal {L}_0(x,\lambda )=r_0(x)\!-q_0(\lambda )\) .
